Finding the Third Proportional to 82,578 and 178,404

Step by Step Solution

1. Step 1: Write the proportion equation
   82,578 : 178,404 = 178,404 : x
2. Step 2: Convert to fraction form
   82,578/178,404 = 178,404/x
3. Step 3: Cross multiply
   82,578x = 178,404 × 178,404
4. Step 4: Simplify right side
   82,578x = 31,827,987,216
5. Step 5: Solve for x
   x = 31,827,987,216/82,578
6. Step 6: Final answer
   x = 385,429.38